1*> \brief \b SGETRF2
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*  Definition:
9*  ===========
10*
11*       RECURSIVE SUBROUTINE SGETRF2( M, N, A, LDA, IPIV, INFO )
12*
13*       .. Scalar Arguments ..
14*       INTEGER            INFO, LDA, M, N
15*       ..
16*       .. Array Arguments ..
17*       INTEGER            IPIV( * )
18*       REAL               A( LDA, * )
19*       ..
20*
21*
22*> \par Purpose:
23*  =============
24*>
25*> \verbatim
26*>
27*> SGETRF2 computes an LU factorization of a general M-by-N matrix A
28*> using partial pivoting with row interchanges.
29*>
30*> The factorization has the form
31*>    A = P * L * U
32*> where P is a permutation matrix, L is lower triangular with unit
33*> diagonal elements (lower trapezoidal if m > n), and U is upper
34*> triangular (upper trapezoidal if m < n).
35*>
36*> This is the recursive version of the algorithm. It divides
37*> the matrix into four submatrices:
38*>
39*>        [  A11 | A12  ]  where A11 is n1 by n1 and A22 is n2 by n2
40*>    A = [ -----|----- ]  with n1 = min(m,n)/2
41*>        [  A21 | A22  ]       n2 = n-n1
42*>
43*>                                       [ A11 ]
44*> The subroutine calls itself to factor [ --- ],
45*>                                       [ A12 ]
46*>                 [ A12 ]
47*> do the swaps on [ --- ], solve A12, update A22,
48*>                 [ A22 ]
49*>
50*> then calls itself to factor A22 and do the swaps on A21.
51*>
52*> \endverbatim
53*
54*  Arguments:
55*  ==========
56*
57*> \param[in] M
58*> \verbatim
59*>          M is INTEGER
60*>          The number of rows of the matrix A.  M >= 0.
61*> \endverbatim
62*>
63*> \param[in] N
64*> \verbatim
65*>          N is INTEGER
66*>          The number of columns of the matrix A.  N >= 0.
67*> \endverbatim
68*>
69*> \param[in,out] A
70*> \verbatim
71*>          A is REAL array, dimension (LDA,N)
72*>          On entry, the M-by-N matrix to be factored.
73*>          On exit, the factors L and U from the factorization
74*>          A = P*L*U; the unit diagonal elements of L are not stored.
75*> \endverbatim
76*>
77*> \param[in] LDA
78*> \verbatim
79*>          LDA is INTEGER
80*>          The leading dimension of the array A.  LDA >= max(1,M).
81*> \endverbatim
82*>
83*> \param[out] IPIV
84*> \verbatim
85*>          IPIV is INTEGER array, dimension (min(M,N))
86*>          The pivot indices; for 1 <= i <= min(M,N), row i of the
87*>          matrix was interchanged with row IPIV(i).
88*> \endverbatim
89*>
90*> \param[out] INFO
91*> \verbatim
92*>          INFO is INTEGER
93*>          = 0:  successful exit
94*>          < 0:  if INFO = -i, the i-th argument had an illegal value
95*>          > 0:  if INFO = i, U(i,i) is exactly zero. The factorization
96*>                has been completed, but the factor U is exactly
97*>                singular, and division by zero will occur if it is used
98*>                to solve a system of equations.
99*> \endverbatim
100*
101*  Authors:
102*  ========
103*
104*> \author Univ. of Tennessee
105*> \author Univ. of California Berkeley
106*> \author Univ. of Colorado Denver
107*> \author NAG Ltd.
108*
109*> \ingroup realGEcomputational
110*
111*  =====================================================================
112      RECURSIVE SUBROUTINE SGETRF2( M, N, A, LDA, IPIV, INFO )
113*
114*  -- LAPACK computational routine --
115*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
116*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118*     .. Scalar Arguments ..
119      INTEGER            INFO, LDA, M, N
120*     ..
121*     .. Array Arguments ..
122      INTEGER            IPIV( * )
123      REAL               A( LDA, * )
124*     ..
125*
126*  =====================================================================
127*
128*     .. Parameters ..
129      REAL               ONE, ZERO
130      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
131*     ..
132*     .. Local Scalars ..
133      REAL               SFMIN, TEMP
134      INTEGER            I, IINFO, n1, n2
135*     ..
136*     .. External Functions ..
137      REAL               SLAMCH
138      INTEGER            ISAMAX
139      EXTERNAL           SLAMCH, ISAMAX
140*     ..
141*     .. External Subroutines ..
142      EXTERNAL           SGEMM, SSCAL, SLASWP, STRSM, XERBLA
143*     ..
144*     .. Intrinsic Functions ..
145      INTRINSIC          MAX, MIN
146*     ..
147*     .. Executable Statements ..
148*
149*     Test the input parameters
150*
151      INFO = 0
152      IF( M.LT.0 ) THEN
153         INFO = -1
154      ELSE IF( N.LT.0 ) THEN
155         INFO = -2
156      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
157         INFO = -4
158      END IF
159      IF( INFO.NE.0 ) THEN
160         CALL XERBLA( 'SGETRF2', -INFO )
161         RETURN
162      END IF
163*
164*     Quick return if possible
165*
166      IF( M.EQ.0 .OR. N.EQ.0 )
167     $   RETURN
168
169      IF ( M.EQ.1 ) THEN
170*
171*        Use unblocked code for one row case
172*        Just need to handle IPIV and INFO
173*
174         IPIV( 1 ) = 1
175         IF ( A(1,1).EQ.ZERO )
176     $      INFO = 1
177*
178      ELSE IF( N.EQ.1 ) THEN
179*
180*        Use unblocked code for one column case
181*
182*
183*        Compute machine safe minimum
184*
185         SFMIN = SLAMCH('S')
186*
187*        Find pivot and test for singularity
188*
189         I = ISAMAX( M, A( 1, 1 ), 1 )
190         IPIV( 1 ) = I
191         IF( A( I, 1 ).NE.ZERO ) THEN
192*
193*           Apply the interchange
194*
195            IF( I.NE.1 ) THEN
196               TEMP = A( 1, 1 )
197               A( 1, 1 ) = A( I, 1 )
198               A( I, 1 ) = TEMP
199            END IF
200*
201*           Compute elements 2:M of the column
202*
203            IF( ABS(A( 1, 1 )) .GE. SFMIN ) THEN
204               CALL SSCAL( M-1, ONE / A( 1, 1 ), A( 2, 1 ), 1 )
205            ELSE
206               DO 10 I = 1, M-1
207                  A( 1+I, 1 ) = A( 1+I, 1 ) / A( 1, 1 )
208   10          CONTINUE
209            END IF
210*
211         ELSE
212            INFO = 1
213         END IF
214*
215      ELSE
216*
217*        Use recursive code
218*
219         N1 = MIN( M, N ) / 2
220         N2 = N-N1
221*
222*               [ A11 ]
223*        Factor [ --- ]
224*               [ A21 ]
225*
226         CALL SGETRF2( m, n1, A, lda, ipiv, iinfo )
227
228         IF ( info.EQ.0 .AND. iinfo.GT.0 )
229     $      info = iinfo
230*
231*                              [ A12 ]
232*        Apply interchanges to [ --- ]
233*                              [ A22 ]
234*
235         CALL SLASWP( N2, A( 1, N1+1 ), LDA, 1, N1, IPIV, 1 )
236*
237*        Solve A12
238*
239         CALL STRSM( 'L', 'L', 'N', 'U', N1, N2, ONE, A, LDA,
240     $               A( 1, N1+1 ), LDA )
241*
242*        Update A22
243*
244         CALL SGEMM( 'N', 'N', M-N1, N2, N1, -ONE, A( N1+1, 1 ), LDA,
245     $               A( 1, N1+1 ), LDA, ONE, A( N1+1, N1+1 ), LDA )
246*
247*        Factor A22
248*
249         CALL SGETRF2( M-N1, N2, A( N1+1, N1+1 ), LDA, IPIV( N1+1 ),
250     $                 IINFO )
251*
252*        Adjust INFO and the pivot indices
253*
254         IF ( INFO.EQ.0 .AND. IINFO.GT.0 )
255     $      INFO = IINFO + N1
256         DO 20 I = N1+1, MIN( M, N )
257            IPIV( I ) = IPIV( I ) + N1
258   20    CONTINUE
259*
260*        Apply interchanges to A21
261*
262         CALL SLASWP( N1, A( 1, 1 ), LDA, N1+1, MIN( M, N), IPIV, 1 )
263*
264      END IF
265      RETURN
266*
267*     End of SGETRF2
268*
269      END
270